A set theoretic analysis of group interactions

Prior to the statistical treatment of experimentally derived data the experimenter must obtain the data. In many studies in psychology, the content of group interactions is obtained by a data coding scheme. Coding schemes are shown to possess hierarchical structures and can be characterized by a hierarchy of fields. Three examples of coding schemes as hierarchies of fields are given. Techniques for extracting numbers from the set are presented. Problems associated with the improper assignment of elements of a data coding scheme to a theoretical structure are examined. The main result is that there will be errors in assignment of data to theory unless the structure of the data coding scheme is identical with that structure which is relevant to the theory being tested. Whenever the structures are not equal, the results are hard to interpret. In fact, any size of assignment error can be obtained. Since these errors precede the usual statistical treatment of data, it would appear that reported empirical findings are only valid when there exists no assignment errors.This research was sponsored by N.S.F. Grant GS-1944.     

Orthogonal rotation algorithms

The quartimax and varimax algorithms for orthogonal rotation attempt to maximize particular simplicity criteria by a sequence of two-factor rotations. Derivations of these algorithms have been fairly complex. A simple general theory for obtaining two factor at a time algorithms for any polynomial simplicity criteria satisfying a natural symmetry condition is presented. It is shown that the degree of any symmetric criterion must be a multiple of four. A basic fourth degree algorithm, which is applicable to all symmetric fourth degree criteria, is derived and applied using a variety of criteria. When used with the quartimax and varimax criteria the algorithm is mathematically identical to the standard algorithms for these criteria. A basic eighth degree algorithm is also obtained and applied using a variety of eighth degree criteria. In general the problem of writing a basic algorithm for all symmetric criteria of any specified degree reduces to the problem of maximizing a trigonometric polynomial of degree one-fourth that of the criteria.This research was supported by the Bell Telephone Laboratories, Murray Hill, New Jersey and NIH Grant FR-3.     

Modification of severe disruptive and aggressive behavior using brief timeout and reinforcement procedures

Brief timeout for disruptive and aggressive behaviors and reinforcement for appropriate behaviors were used with two retarded patients in a state hospital ward setting. The procedures reduced loud vocal behavior in one patient and aggressive behavior in another to near-zero levels when first applied. The behaviors returned to previous levels when the procedures were removed and were again greatly reduced when timeout and reinforcement were reapplied. The results were significant because the behavior problems were severe and long-standing and the procedures were instituted without greatly disturbing normal ward routine.